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Question
Inside a square field of side 44m, a square flower bed is prepared leaving a graved path all round the flower bed. The total cost of laying the flower bed at Rs.25per sq m. and gravelling the path at Rs.120per sq m. is Rs.80320. Find the width of the gravel path.
Solution
Let the width of the gravel path = `x/(2)"m"`
Now, Area of flower bed (shown in Pink) x 25 + Area of gravel path(Shown in Yellow) = Rs.80320
i.e (44 - x)2 x 25 + [442 - (44 - x)2 x 120 = 80320
(44 -x)2 x 25 + 442 x 120 - (44 - x)2 x 120 = 80320
(44 - x)2 x (25 - 120) + 442 x 120 = 80320
(44 - x)2 x (-95) + 1936 x 120 = 80320
(44 - x)2 x (-19) + 1936 x 24 = 16064
46464 - 1664 = 19(44 - x)2
30400 = 19(44 - x)2
(44 - x)2 = 16000
44 - x = 40
x = 4
the width of the grave path = `x/(2)` = 2m.
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